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Abstract
The size of the concept lattices increases exponentially from the number of objects and attributes. This situation is more complicated in the fuzzy case, in which the considered carriers to evaluate the objects and attributes, and for the relation, are also taken into account. Hence, it is very important to study mechanisms to reduce the size of fuzzy concept lattices maintaining the main information. One of the most important mechanisms to reduce the size of concept lattices is the use of thresholds in the concept-forming operators. This paper studies this mechanism in the general fuzzy framework of multi-adjoint concept lattices, obtaining interesting properties and consequences.
Acknowledgements
This work has been partially supported by Junta de Andalucí a grant P09-FQM-5233, and by the EU (FEDER), and the Spanish Science and Education Ministry (MEC) under grants TIN2009-14562-C05-03 and TIN2012-39353-C04-04.
The author would like to thank the anonymous referees for their careful reading of the paper and many useful suggestions to clarify this work.
Notes
1. Note that, given an adjoint conjunctor, its adjoint implications are unique, hence the adjoint conjunctors only need to be fixed in a multi-adjoint frame.
2. More information about this notion of preference is given in [Citation32].
3. The definitions of infimum-dense and supremum-dense are well known and they can be found in [Citation32].